what's the thickness of a rectangle prism with a height of 12 inches, a width of 8 inches and surface area 992 square inches?
1 answer:
Answer:
Thickness of rectangle prism is <em>20 inches.</em>
<em></em>
Step-by-step explanation:
Given:
Surface area of rectangular prism, A = 992 sq inches.
Height, h = 12 inches
Width, w = 8 inches
To find:
Thickness / length of prism, = ?
Solution:
First of all, let us learn the formula for surface area of a rectangular prism.
Formula for surface area of a prism is given as:
As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.
Putting all the given values in the formula to find the value of :
So, the answer is Thickness of rectangle prism is <em>20 inches.</em>
You might be interested in
Answer: Choice B) between 6:48 AM and 5:12 PM
=========================================================
Explanation:
I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.
We want to find values of t that satisfy f(t) > 25
This is the same as trying to solve f(t) - 25 > 0
So we have,
To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.
Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.
Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)
Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.
When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.
Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.
Then focusing on the point (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours
1700 hours in military time = 17-12 = 5 pm
The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.
We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).
--------------------------
In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.
Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.
